WPF

<Window x:Class="DataGrid.Window1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:dg="http://schemas.microsoft.com/wpf/2008/toolkit"
    Title="Window1" Height="300" Width="300">
    <Grid>
        <Grid.RowDefinitions>
             <RowDefinition Height="*" />
             <RowDefinition Height="*" /> 
             <RowDefinition Height="9*" /> 
         </Grid.RowDefinitions>
             <ColumnDefinition Width="*" />
             <ColumnDefinition Width="*" />
        <Grid.ColumnDefinitions>

        </Grid.ColumnDefinitions>

        <dg:DataGrid x:Name="dataGrid" 
                     Grid.Row="3" 
                     Grid.ColumnSpan="2"
                     SelectionChanged="dataGrid_SelectionChanged" 
                     Grid.Column="0" 
                     CanUserDeleteRows="True" 
                     Loaded="dataGrid_Loaded"
                     IsReadOnly="True" 
                     SelectionUnit="FullRow" 
                     SelectionMode="Single" 
                     CanUserAddRows="False" 
                     Visibility="Visible"
                     Margin="1" 
                     Background="White" 
                     AlternationCount="2" />
        <TextBox Name="textBox1" Grid.Row="0" Grid.ColumnSpan="2" />
        <Button Grid.Row="1" Name="Add" Click="Add_Click">Add address to DataGrid</Button>
        <Button Grid.Column="1" Grid.Row="1" Grid.RowSpan="2" Name="Delete" VerticalAlignment="Top" Click="Delete_Click">Delete selected row</Button>
    </Grid>
</Window>

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;
using System.IO;
using System.Collections.ObjectModel;

namespace DataGrid
{
    public partial class Window1 : Window
    {

        ObservableCollection<files> obs_col;
        public Window1()
        {
            InitializeComponent();
            obs_col = new ObservableCollection<files>();
        }


        private void dataGrid_Loaded(object sender, RoutedEventArgs e)
        {
            dataGrid.ItemsSource = obs_col;
        }


        private void dataGrid_SelectionChanged(object sender, SelectionChangedEventArgs e)
        {
            Files selectedFile = (Files)dataGrid.SelectedItem;

            if (selectedFile != null)
            {
                if (!File.Exists(selectedFile.File))
                {
                    obs_col.RemoveAt(obs_col.IndexOf(selectedFile));
                }
            }
        }


        private void Add_Click(object sender, RoutedEventArgs e)
        {
            obs_col.Add(new Files(textBox1.Text));
        }


        private void Delete_Click(object sender, RoutedEventArgs e)
        {
            Files selectedFile = (Files)dataGrid.SelectedItem;

            if (selectedFile != null)
            {
                obs_col.RemoveAt(obs_col.IndexOf(selectedFile));
            }
            else
                MessageBox.Show("No row is selected");
        }
    }
}</files></files>

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace DataGrid
{
    class Files
    {

        public string File
        {
            get; set;
        }

        public Files(string file)
        {
            this.File = file;
        }

    }
}